March 10th, 2017, 12:02 AM  #1 
Member Joined: Mar 2016 From: Sweden Posts: 34 Thanks: 4  Stokes theorem
I am trying to figure out when and how to use Stokes theorem. I was looking at this video: and I am really confused about how he uses the theorem. About 4.30 he writes down the integral using Stokes. So if I am having a cylinder and some line integral around it. Then it doesn't matter how this line integral looks like? Seems like he is having some arbitrary line integral around that surface.. Thx! 
March 10th, 2017, 03:50 AM  #2 
Member Joined: Dec 2016 From:  Posts: 61 Thanks: 10 
Stokes theorem works in the following way: Imagine you have a vector field $\vec{A}$, and you want to calculate the integral along a path $\gamma$ (in your case, this can be the integral along a line surrounding the cylinder). Then the following holds: \begin{eqnarray} \int_{\gamma}d\vec{s}.\vec{A}=\int_{S}d\vec{S}. \vec{\nabla}\times \vec{A} \end{eqnarray} where the integral on the right hand side is over the surface $S$, and $dS$ is the differential normal surface vector. This equality holds regardless of the geometry of the problem under consideration, so it is completely general. Hope it helps 

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